Comparative Study of Experimental and Theoretical Model of...

JOURNAL OF SEMICONDUCTOR TECHNOLOGY AND SCIENCE, VOL.17, NO.6, DECEMBER, 2017 ISSN(Print) 1598-1657

https://doi.org/10.5573/JSTS.2017.17.6.878 ISSN(Online) 2233-4866

Manuscript received Apr. 11, 2017; accepted Aug. 7, 2017 1 Semiconductor Laboratory, Nanostructures And Advanced Technology at CRTEn, Tunis,Tunisia 2 University of Sciences of Manar, Tunis, Tunisia

E-mail : [email protected], [email protected],

[email protected]

Comparative Study of Experimental and Theoretical

Model of Highly-efficient GaInP/Si Tandem Solar Cells

Rached Ganouni1,2

, Mourad Talbi1, and Hatem Ezzaouia

1

Abstract—Si based tandem solar cells speak to a

contrasting option to conventional compound III-V

multi-junction cells as a promising approach to

accomplish high efficiencies. In this paper, we

compare between an experimental model of a novel 4-

terminal tandem cell design with a back-junction

back-contacted (BJBC) c-Si and a theoretical model

(proposed in this work) of a new structure of tandem

solar cell based on c-Si using Matlab code. The

obtained results from the computation of the overall

efficiency η, show that we can attain the same

efficiency (η = 28%) compared to the experimental

model, but with less cost. Moreover, the physics

coherence problem is solved with our model.

Index Terms—Tandem solar cell, c-Si, efficiency,

BJBC

I. INTRODUCTION

Multijunction solar cells based on III-V

semiconductors are promising as a good innovation for

next generation high-efficiency solar cells [2]. Given that

Si is the most popular semiconductor material in the

practical photovoltaic. Therefore, it is better to use the Si

in fabrication of multi-junction cells. However, III-V-on-

Si multi-junction cells cannot be easily fabricated for

many reasons, as an example the difference in lattice

constant and thermal expansion coefficients between III-

V materials and Si [3]. To solve this problem, in this

paper we propose a new architecture between III-V

materials and Si.

In this work we will make a comparison between

experimental model of a novel 4-terminal tandem cell

design with a back-junction back-contacted (BJBC) c-Si

[1] and a new provision of tandem solar cell by a model

that will describe an innovation in the field of

photovoltaic and avoiding the problems already

announced. This model is based on a rigorous theoretical

calculation using Matlab code (including optical and

electrical modules). This study focus on the design of a

two junction GaInP/c-Si solar cell, under the standard

AM1.5 solar spectrum, including the design of separation

of cells in order to avoid the problem of mismatch

between c-Si and III-V materials. Finally we will

determine the reflectance, current density and efficiency

of this new model and compare it to the experimental

model [1].

II. THEORETICAL APPROACH

1. Introduction of Model

In this paper we propose a new model of GaInP/c-Si

tandem solar cell based on parabolic trough concentrator.

This model is illustrated in Fig. 1.

As shown in Fig. 1, this model is constitutes of two

parabolic systems. The first parabolic system includes a

single region 2 located between two regions 1 having the

same surface and each of them contains a reflector with

95% of reflexion (composed by Al2O3 + nSi(PECVD)).

The region 2 contains a c-Si single junction solar cells

JOURNAL OF SEMICONDUCTOR TECHNOLOGY AND SCIENCE, VOL.17, NO.6, DECEMBER, 2017 879

connected in series. Each of these solar cells is modeled

in Fig. 2. The second parabolic system contains a GaInP

single junction solar cells connected in series, each of

these solar cells is modeled in Fig. 2.

Each of GaInP or c-Si cell is composed by absorbent

layer TiO2, p-n junction and reflective layer Al2O3 (Fig.

2(a) c-Si single junction solar cells and (b) GaInP single

junction solar cells).

The solar radiation arriving on both regions (1) of the

first parabola will undergo a total reflection to arrive at

the second parabola. A large part of the spectrum will be

absorbed by the cell of large gap GaInP, the rest is

reflected from this cell to be absorbed by the cell c-Si.

Light is reflected by the back surface of c-Si and we win

the most of energy. The study of our structure is based on

the calculation of three fundamental terms. Reflectance

R, external quantum efficiency QE and current density J.

The optical demonstrating proposed in this paper

depends on the transfer matrix formalism. It permits

calculation of the incident optical spectrum on each

subcell from the solar cell spectrum. Each layer of the

multi-junction is depicted by a transfer matrix M which

is characterized by

M =11 12

21 22

m m

m m

=( ) ( )

( ) ( )

j

j

j

j j j

i sincos

N

i N sin cos

δδ

δ δ

(1)

With

jδ =

2

j

j

Nd

π

λ; ( ) ( )λ λ

j j jN n i k= +

Fig. 1. New model of tandem solar cells with parabolic trough concentrator (In French: concentrateur cylindro-parabolique).

Fig. 2. Composition of GaInP and c-Si solar cells.

880 RACHED GANOUNI et al : COMPARATIVE STUDY OF EXPERIMENTAL AND THEORETICAL MODEL OF HIGHLY-EFFICIENT …

where ( )λjn , ( ) λ

jk and j

d are the refraction,

extinction index and the thickness of the layer

respectively. λ is the wavelength. The reflectance

coefficient R [4, 5] of the layer is then given by

R = 2

r =

2

0 11 0 12 21 22

0 11 0 12 21 22

s s

s s

n m n n m m n m

n m n n m m n m

+ − +

+ + + (2)

where n0 is the superstrate refractive index and ns is the

substrate refractive index. The ,j nm coefficients refer to

the matrix transfer elements. Thus, it is possible to search

the appropriate thickness of layer to calculate QE and J.

Multi-junction cells act like homojunction cells in

series, and their open circuit voltage is the aggregate of

the voltages of the subcells, while their short circuit is

that of the subcell with the lowest current. Thus, the

execution of a multi-junction cell can be acquired from

the execution of each subcell assessed freely. For each

subcell, the load current density J is given by the

superposition of two diode currents and the photo-

generated current [6],

phJ J= – 01

J 1)(qVkTe − – 02

J 2 1)(qV

kTe − (3)

where

phJ is the photocurrent density , J01 is the ideal dark

saturation current component, and J02 is the space charge

non-ideal dark saturation current component.

k is the Boltzmann constant

q is the electron charge

T the temperature (T = 25°C) and V the voltage.

The photocurrent density is given by the aggregate of

the photocurrents created in the emitter, the base and the

depleted region of the cell. Also, the dark current density

is given by the entirety of the dark currents produced in

the emitter, the base and the depleted region of the cell

[6], we have:

phJ

emitterJ= + base

J + depletedJ , (4)

This model incorporates optical and electrical modules,

with the optical modules permitting the examination of

the appropriate thickness for each layer ( jx , B

x ,

x (TiO2) and x (Al2O3)) of GaInP and c-Si. At that point,

the electrical model computes the photocurrents in the

space charge region, the emitter and the base for every

junction.

2. Solar Cell Structure and Parameters

The wavelength-dependent reflectance coefficient of

GaInP and c-Si is based on the research of fitting curves

of the exctinction coefficient, ( )λjn and the refractive

index, ( ) λjk .

The fit for this curves [7-9] is given by :

* n( λ ) [GaInP] = 3.26 +( )28916.49

216094 408

+−λ

;

* k( λ ) [GaInP] = -0.0169 +( )2

3452015672

4 334.2+

−λ.

* n( λ ) [c-Si] = 3.31+9.46.* exp(-0.0042.* λ );

* k( λ ) [c-Si] = -0.074+ 263.54.*exp(-0.0136.* λ ).

* n( λ ) [TiO2] = 2.59+1.71( ) ( )325.98

38.99325.98

138.99

e

e

λλ

− − − − −

* k( λ ) [TiO2]

= 1.167-1.162 ( ) 1coth 336.26

336.26λ

λ

− − −

* n( λ ) [Al2O3][10] = 2.29623 + ( )532.1490

35.08544

0.17963

1 e

−

+λ

* k( λ ) [Al2O3] = 0

The incident photon flux F for AM1.5 spectrum is

taken by a fitting curve [11].

F = ( )Ecl

hc

λ

λ (5)

Ecl ( )λ =( ) ( )2.28411

0.26053 0.26053

0.15994 0.22850.06977 7.0625 1 e e

λ λ− − − − + −

For 300 nm λ< < 1400 nm (6)

where Ecl ( ) λ (KW/m2µm) the illumination, h Planck

constant, c velocity of light.

The incorporated ASTM Sub-commitee G3.09 AM1.5

solar spectral irradiance has been made to adjust to the

estimation of the solar constant acknowledged by the


space community, which is 694 W/m².

The diverse factors of c-Si and GaInP are

characterized in Tables 1 and 2.

The absorption coefficient of GaInP [13] can be fitted

by

α(GaInP) =5.5 g gE E 1.5 E E 1− + − − (7)

The absorption coefficient of c-Si [15] can be fitted by

α(c-Si) =0.0312+0.00114.*exp(2.88.*E) (8)

where E is the photon energy and Eg is the fundamental

band gap, both in eV, and α in 1/µm.

3. Simulation and results

In this section we have varied the thickness of each

layer in order to have from Matlab simulation, a suitable

reflectance curve for each cell and this by referring to the

ideal theoretical curve. In Fig. 3(a) and (b), are illustrated

the reflectance curves obtained from Matlab simulation

and from the theoretical formula given as follow [16]:

( )( )

1.24

g

g

E eVmλ µ

= (9)

where ( )gE eV and ( )g

mλ µ are band gap energy and

wavelength respectively. This formula explains the

variation of ( )gE eV vs ( )g

mλ µ (Red curve in Fig.

3(a) and (b)). For c-Si, ( )gE eV = 1.1, this mean that

( )gmλ µ = 1.12. This result explain that c-Si absorb for

1127nmλ < (Reflectance = 0) and reflect all light for

1127nmλ > (R 1)≅ . For GaInP, ( )gE eV = 1.86, this

mean that ( )gmλ µ = 0.66. This result explain that

GaInP absorb for 660nmλ < (Reflectance = 0) and

reflect all light for 660nmλ > (R 1)≅ .

The simulation curve give for c-Si 592jx nm=

750Bx nm= , ( )2

16i

x TO nm= , ( )2 30 7x Al nm= and

for GaInP 59jx nm= , 188

Bx nm= , ( )2

75i

x TO nm= ,

( )2 30 210x Al nm= .

Table 1. Values for the parameters of c-Si [12] and GaInP [13]

used in the model calculation

Parameters c-Si GaInP

Band gap Eg(ev) 1.1 1.86

The electron surface recombination

velocity Sn(cm/s) 10² 1.7 106

The hole surface recombination velocity Sp(cm/s)

103 104

Electron diffusion length Ln(µm) 646 3

Hole diffusion length Lp(µm) 1.18 0.5

Electron diffusion coefficient

Dn(cm²/s) 41.8 100

Hole diffusion coefficient Dp(cm²/s) 1.39 5

Table 2. Values for the parameters c-Si [12] and GaInP [14]

used in the model

Parameters c-Si GaInP

Concentration of acceptors NA(cm-3) 2*1015 1018

Concentration of donors ND(cm-3) 1.25*1017 1017

Intrinsic carrier concentration (cm-3) 4.29*1010 1.9 10²

Permittivity 11.6 11.8

(a)

(b)

Fig. 3. The reflectance curve of (a) c-Si, (b) GaInP.


Fig. 3 demonstrates the ideal intelligibility amongst

theoretical and simulation proposed, along this line the

absorption of c-Si is important in the scope of

wavelength 300-1127 nm, whereas for GaInP is in the

scope of 300-650 nm. This outcome is critical to the

following work, along this lines we can with the

estimations of thickness jx and B

x represent the curve

of external quantum efficiency and density of current.

Fig. 4 and 5 demonstrate the aggregate total external

quantum efficiencies QE and the integrated photocurrent

density phJ of the two cells computed from Eq. (4). The

external quantum efficiency is a component of

wavelength, and the photocurrent density phJ is

acquired from the integral of the product of quantum

efficiencies (We can use too this rule [4]: phJ =

( )( )1

n

ph i

i

J λ=∑ ).

The high band gap cell GaInP generates a photocurrent

density of 16 mA/cm², the low bandgap cell c-Si

generates only 9.2 mA/cm².

Fig. 6 show I-V characteristics for each subcell c-Si

and GaInP. For the case of a cell with the new structure

without tunnel junction and with a serie connection

between sub-cells, Jsc, Voc, FF and conversion efficiency

η were determined for each of the junctions. Fig. 7 shows

the J–V curves for each of the sub-cells and the tandem

cell in the new model.

These curves for the series-connection cells was made

using the equivalent circuit for 2 cells in series, phJ

(GaInP) = phJ (GaAs) = ph

J (Series-connection model) =

9.2 mA/cm². The resultant J–V and is shown in Fig. 7.

These results are summarized in Table 3. For the

proposed tandem solar cell : Jsc = 9.2 mA/cm², Voc =

2.4 V, FF = 0.94 and η = 28%. This is expected high

conversion efficiency under the AM1.5 solar spectrum,

comparable to current technology two junction solar cells,

and there for the GaInP/c-Si solar cell studied here is an

attractive alternative for high efficiency solar energy

conversion.

Fig. 4. The external quantum efficiency of c-Si and GaInP.

Fig. 5. Integrated photocurrent density of c-Si and GaInP.


Fig. 6. I-V characteristics of GaInP and c-Si under AM1.5.

Fig. 7. I-V characteristics of the series-connections between

GaInP and c-Si under AM1.5.

Table 3. Calculated current densities, open circuit voltage, fill

factor, and power conversion efficiency for each of the sub-

cells and for the full cell of new model

Solar cell Jsc(mA/cm²) Voc(V) FF η (%)

c-Si 9.2 0.6 83 6.4

GaInP 9.2 1.8 89 21.2

Series connection model

(GaInP with c-Si) 9.2 2.4 94 28

III. EXPERIMENTAL MODEL

Our theoretical model is compared to an experimental

model based on a novel 4-terminal tandem cell design

with a back-junction back-connected (BJBC) c-Si bottom

cell [1]. The structure of this experimental model is

shown in Fig. 8,

IV. RESULTS AND DISCUSSION

To compare the two models we prepare the curve of

each in the same axis. Fig. 9 and 10 shows the external

quantum efficiency and the curve I-V of the two models.

Result of comparison is given in the Table 4.

Compared to the experimental model [1], the

theoretical model without direct contact of the two

materials permits to obtain lower efficiency with c-Si cell,

and higher efficiency with GaInP cell, respectively.

Moreover, the overall efficiency, η, has been improved.

Higher efficiencies can be achieved with our

theoretical tandem solar cell model. The experimental

model [1] suffers from a low fill factor, FF, of 60.5%

(for the bottom cell) caused by damage induced during

the processing of the top cell and series resistances losses,

this problem is resolved in our theoretical model by no

connection directly between Si and GaInP. So we arrived

to a fill factor, FF, greater than 80%.

V. CONCLUSION

The experimental model shows that mechanically

stacked GaInP/c-Si tandem solar reached an efficiency of

27%.Whereas with our new structure we show that we

Fig. 8. Structure of the simplified GaInP on Si tandem solar cell

being investigated with 4T configuration.


can arrived to efficiency greater than 27 % and with less

cost of fabrication and less problem of coherence

between materials. So we can say that this theoretical

model is an innovation in the field of tandem solar cells

Si / III-V materials.

REFERENCES

[1] Stephanie Essig, Scott Ward, Myles A. Steinler ,

Daniel J.Friedman, John.Geisz, Paul Stradins,

DavidL.Young, '' Progress towards a 30% efficient

GaInP/Si tandem solar cell ''. Energy Procedia.

[2] Hector Cotal, Chris Fetzer, Joseph Boisvert,

Geoffrey Kinsey, Richard king, Peter Hebert,

Hajoun Yoon and Nasser Karam, ''III-V

multijunction solar cells for concentrating

photovoltaics", Energy Environ. Sci., 2009, 2, 174-

192. DOI : 10.1039/B809257E.

[3] Green, M.A., Cho, E.-C., Cho, Y., Huang, Y., Pink,

E., Trupke, T., Lin, A., Fangsuwannarak, T.,

Puzzer, T., Conibeer, G. and Corkish, R. '' All-

silicon tandem cells based on 'artificial'

semiconductor ssynthesised using silicon quantum

dots in a dielectric matrix.'' Proc. 20th European

Photovoltaic Solar Energy Conf. (Barcelon, Spain).

2005.

[4] F. Dimroth, C. Baur, A.W. Bett, M. Meusel, G.

Strob, 31st IEEE Photovoltaic Specialists

Conference (PVSC-2005), 525 (Orlando, USA:

2005).

[5] Masafumi Yamaguchi*, III–V compound multi-

junction solar cells: present and future, Solar

Energy Materials & Solar Cells 75 (2003) 261–269.

[6] Lin Guijiang, Wu Jyhchiarng, and Huang Meichun,

''Theoritical modeling of the interface

recombination effect on the performance of III-V

tandem solar cells'', Journal of Semiconductors,

2010. Vol. 31, No.8 .

[7] Fahrenbruch A L, Bube R H. Fundamentals of solar

cells photovoltaic solar energy conversion. New

York: Academic Press,1983.

[8] Wurfel P. Physics of solar cells: from principles to

new concepts.Wiley-VCH, 2005

[9] Refractive index and extinction coefficient of

materials (book).

[10] Handbook of optical materials.

[11] Refractiveindex.info, refractive index database .

[12] Stéphane COUTANSON, Study Of Laser Doping

In Phases Solid And Liquid :Application In The

Joints Of Training Ultra - Thin In Silicon (Thesis

written in French).

[13] Souici Fatma-Zohra, Modélisation d’une cellule

solaire en couche mince à base de Cuivre Indium

Fig. 9. The comparison between experimental and theoretical

external quantum efficiency of tandem solar cell GaInP/c-Si.

Fig. 10. The comparison between experimental and theoretical

curve I-V of tandem solar cell GaInP/c-Si.

Table 4. Calculated current densities, open circuit voltage, fill

factor, and power conversion efficiency for each of the sub-

cells and for the full cell of new model compared to the

experimental model.

Solar cell Jsc(mA/cm²) Voc(V) FF η (%)

c-Si(theoritical) 9.2 0.6 83 6.4

GaInP(theoritical) 9.2 1.8 89 21.2

Series connection

model(GaInP with c-Si)

(theoritical)

9.2 2.4 94 28

c-Si(experimental [1]) 23.3 0.605 60.5 8.54

GaInP(experimental [1]) 14.6 1.44 87.9 18.54

Total of experimental

model [1] 27


Sélénium(CuInSe2), faculte des sciences et

sciences de l'ingenieur, Université Kasdi Merbah

Ouargla.

[14] Alain Ricaud, solar cells, The physics of the

conversion photovoltaique to filiers materials and

processes, page180. (book in French).

[15] Handbook_of_Photovoltaic_Science_and_Engineer

ing, page 73.

[16] S. Petibon; « nouvelles architectures distribuées de

gestion et de conversion de l’énergie pour les

applications photovoltaïques » Université de

Toulouse _ LAAS, Septembre 2009.

Rached Ganouni is a bachelor

degree in physics sciences and

obtained his master degree in 2010

from Faculty of Sciences of Tunis.

He is actually a researcher in (Center

of Research and Technologies of

Energy of Borj-Cedria,Tunis,Tunisia).

He works on tandem solar cells based on III-V materials.

Mourad Talbi is an Assistant

professor in center of researches and

technologies of energy, Tunis, Tunisia.

He received the Ph.D. Thesis (2010)

and the HDR (2016) in Electronics

from Faculty of Sciences of Tunis.

Hatem Ezzaouia Postgraduate

Degree Physics of solids and Physics

of semiconductors - Paris 11

University SUPELEC & CNRS

(LPS) in France June 1980. -

Doctorate in Physics of solids Paris

11 University & CNRS (LPS) France

June 1982. – (HDR) University Habilitation in Physics

(Faculté des Sciences de Tunis 1999 Tunisia) Manar

University. -Post-Doc at the NATIONAL CENTRE FOR

SCIENTIFIC RESEARCH (LPS-CNRS-MEUDON-

PARIS-FRANCE) from 1982 to 1985. – Assistant at the

NATIONAL INSTITUT FOR SCIENTIFIC RESEARCH

AND TECHNOLOGIES (INRST) in Tunisia from 1986

to 1989. - Assistant Professor at the INRST from 1989 to

1999. - Full Professor at the INRST from 1999 to 2004. -

University Professor at the INRST in 2004

• 1999 - 2001 Lab Director of LAS (INRST Solar

Applications Laboratory)

• 2002 - 2005 Lab Director of LPVS (INRST

Photovoltaic Laboratory and Semiconductors)

• 2006 - 2009 Lab Director of LPVSN (Photovoltaic

Laboratory Semiconductors and Nanostructures at

CRTEn)

• 2015 Lab Director of LSNTA (Semiconductor

Laboratory, Nanostructures And Advanced Technology

at CRTEn)

Comparative Study of Experimental and Theoretical Model of...

Documents

Transcript of Comparative Study of Experimental and Theoretical Model of...